Dynamics of expanding slug ow bubbles in non-newtonian drilling uids

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ANNUAL TRANSACTIONS OF THE NORDIC RHEOLOGY SOCIETY, VOL. 19, 2011 Dynamics of expanding slug ow bubbles in non-newtonian drilling uids A. H. Rabenjamanantsoa, Rune W.

1 ANNUAL TRANSACTIONS OF THE NORDIC RHEOLOGY SOCIETY, VOL. 19, 2011 Dynamics of expanding slug ow bubbles in non-newtonian drilling uids A. H. Rabenjamanantsoa, Rune W. Time, Thomas Paz University of Stavanger, Norway ABSTRACT The motion of expanding slug bubbles in near vertical ows is investigated for non-newtonian liquids simulating drilling uids. It is a challenge both from engineering points of view and for theoretical-numerical simulations of slug ow to know how the gas bubbles trailing a Taylor bubble will spread along the tail of the bubble. A very important industrial example is gas-kicks during drilling of petroleum wells. The inuence of main parameters including shear conditions and turbulence intensity at the rear of the bubble, as well as the ability of the uid to keep the trailing bubbles in suspension were investigated. The experiments were done using high speed camera and PIV technique in a 5 meter high pipe of 8 cm inner diameter. Comparisons were done between Newtonian and non-newtonian uids. Dierent initial pressures in the slug bubbles were used to investigate transient eects. as gas kick in oil and gas wells and geothermal fermentation, among others 1,2. The slug can in some situation give ecient mixing by taking prot from the wake region. TAYLOR BUBBLE Following the description of Das et al. 3, a Taylor bubble in a circular pipe is symmetric about the vertical axis and comprises two regions, see gure 1. As seen in INTRODUCTION Dierent ow patterns occur through a vertical conduit during simultaneous owing of liquid and gas. One of these ow patterns is slug ow. Such ow pattern is characterized by an alternate owing of large bubbles, known as Taylor bubbles, separated by liquid slugs. This type of ow is identied in engineering applications, such Figure 1: Photograph of a Taylor Bubble. gure 1 the upper part is the nose region and the lower part the tail region. The shape of the nose region is spherical while that of the tail region is cylindrical. The

2 owing liquid around the bubble forms a falling lm under gravity. The end of the bubble is separated from this lm and creates a liquid wake. This is attached to the bubble rising and the pipe wall. This lm creates a vortex as it merges to the surrounding liquid below,i.e at the rear of the bubble. An universal correlation for the rise velocity of long gas bubbles in round pipe has been compiled 4. It was found that: U = K gd (1) where, U is bubble velocity K is an empirical value about 0.351, D is pipe diameter, and g is acceleration due to gravity This equation has been mentioned 4 to be a result of a large amount of compiled data by Dumitrescu in 1943 and further investigated by several authors. The goals of this work was to compare eects on Taylor bubbles in Newtonian versus non-newtonian systems, as well as to determine the dynamics of quickly expanding bubbles. EXPERIMENTAL Experimental facility The study was performed in the experimental setup schematized in gure 2. The facility consists mainly by an acrylic cylindrical pipe of 3.6 m height, H 1 and 8 mm internal diameter. The top of the pipe is made opened to the atmosphere. Another tube, H 3 is connected beneath the main column. A ball valve, H 2 is attached between these two pipes to facilitate the launch of a Taylor bubble. Another pipe L is further connected to the setup in order to make drainage easy during change of dierent uid systems. Four dierential pressure stations (P 0, P 1, P 2, P 3 ), as seen in gure 2 were mounted to the pipe. They were located at 1m apart from each other except from P 0 which was situated at 9cm H 3 = 135cm H 1 = 360cm Valve P 3 P 2 P 1 P 0 Cylinder lenses DP 1 DP 2 DP 0 L = 207 cm CW Laser t 0 t 1 Particle images Air feed LCD 2500S High speed camera Correlation Velocity vectors Liquid drainage Figure 2: Schematic representation of the bubble transport system. beneath the valve. A T-joint is connected to this station for air injection. The volume of bubble is controlled by closing the valve. Air is then injected to substitute approximately 700mL of drained liquid. The section below the valve can be pressurized in order to create initial conditions where a bubble expands more than if just starting to rise in stagnant liquid. Dierential pressures P 1 measures the pressure dierence between the pressure stations P 2 and P 1, while P 2 measures the pressure dierence between the pressure stations P 3 and P 2. P 0 measures the pressure at P 0 relative to the atmosphere. When a bubble passes the pressure stations, the dierential pressures drops instantly. The bubble velocity can then be determined from the time of its passage between the dierential pressure stations. The distance between two stations is, as mentioned set to H = 1m. From the P signals the bubble velocity and length could be determined since

the distance between the P locations are known. When the signal drops quickly, the bubble nose passes the pressure stations, as illustrated in gure 3.

The viscosity of the uids used is presented in gure 4. Figure 3: Illustration of the P signals when the bubble nose passes two pressure locations.

3 the distance between the P locations are known. When the signal drops quickly, the bubble nose passes the pressure stations, as illustrated in gure 3. t is the time dierence between t 2 and t 1 which are relative to P 2 and P 1 locations. The viscosity measurements were taken after the tests have been run. The viscosity of the uids used is presented in gure 4. Figure 3: Illustration of the P signals when the bubble nose passes two pressure locations. LabView package was designed for the recording of the P's. The scan rate was set to 250Hz. The visual test section was located at approximately 50 cm from the top of the tube. This was chosen to assure that the ow is well established. The analysis of the experimental results is aimed at describing the detailed features of the ow using both Newtonian and non- Newtonian uids. Fluid rheology Two dierent concentrations of polyanionic cellulose, PAC regular obtained from MI- Swaco, were used: 200 and 400 ppm PAC dissolved in water. A dispermix - stator on struts and foot bearing, type Shaft MD- LDT 1 connected to an Ystral motor from Maschinenbau + processtechnik was used for the preparation of the solution before pouring to the tube. The rheological measurements were taken using a Physica UDS 200 rheometer with cone plate conguration MK 24 (75 mm, 1 o ). The two samples were measured at 20 o C with increasing shear rate to the maximum (1022 s 1 ) and decreasing again to the minimum (1.5s 1 ). This was chosen to see any hysteresis effect. Figure 4: Viscosity versus shear rate at 20 o C of the 200 and 400 ppm concentrations of PAC dissolved in water. For each solution, the focus was on Taylor bubble with a volume of approximately 700 ml air, as mentioned earlier. This is considered to be a sucient length and that the liquid falling lm owing around the bubbles has developed. Image analysis The PIV technique is described by Rabenjamanantsoa 6 et al. but we recall it here for brevity. The PIV system includes a Suwtech continuous wave (CW) diode laser giving a beam with 532nm wavelength. The beam is collimated into a 1mm thick and 5cm wide, nearly parallel "light sheet", using two cylinder lenses. The beam energy is adjustable up to 200mW using a Photop LDC-2500S power supply. A high speed camera (MiniVis e2, 512x512 pixels, 2500 fps) was computer controlled using the software program MotionBlitz from Mikrotron, to record series of pictures. Acquired images from the MiniVis camera were imported in DynamicStudio 7 version 2.10 from DantecDynamics for postprocessing. The processing unit performs picture analysis to determine particle velocity based on a two-dimensional cross correlation technique. In addition, light emitting diodes (LEDs) were also setup in some situ-

4 ations. In this work, the interrogation windows was 32x32 pixels with 50% overlap. MatPIV 8 version was also used in postprocessing the images. The detail performance of this Matlab toolbox is explained in Rabenjamanantsoa 9, but briey recalled here for clarity. Pairs of images were used for calculation of velocities in the (x,y)-plane. The velocities were obtained by a four step cross correlation calculation (64x64, 32x32, 16x16, 16x16, 50% overlap). This is achieved using the 'multin' option (multiple pass analysis) which calculates the PIV vectors using 4 iterations starting from 64x64 windows and nishing with 16x16. The scale factor which is the conversion from pixels to the 'real world' co-ordinates was obtained from DynamicStudio. EXPERIMENTAL RESULTS Figure 5 shows the P signals from water ow when the bubble passes through the pressure stations (top) and the pressure applied during the release. This was clearly illustrated in gure 3. The plot in gure 5 shows a "running time average" of original pressure recordings at 250 Hz sampling rate, together with error bands given by one standard deviation. For the plot is used the average of 20 recordings, centered within each time segment. As seen in gure 5 (top) and referring to gure 3, the P 's are zero and the P 0 is measured to be 650mbar. At approximately 3.5s abrupt increases in P 1 and P 2 is observed. At the same time P 0 decreases to approximately 325mbar. This is the time of release of the bubble. The observed permanent loss is due to two factors; the release from the pressurized section below the valve, and the gas trapped and released as the Taylor bubble. In gure 5 (top), two datatips are displayed, P 1 (6.764) and P 2 (10.12). They show the respective time and P when the bubble nose has traveled 1m. At these times, the P 's drop abruptly indicating that the Figure 5: P signals in water ows showing the passage of the bubble between two pressure stations (top) and the pressure applied to the bubble during release (bottom). bubble nose has passed the pressure stations. Knowing that the stations are located at 1m apart from each other, it can be calculated that the bubble velocity is equal to be m/s. In addition, applying the equation (1) the bubble velocity is calculated to be 0.31 m/s. The ow eld ahead of the Taylor bubble nose were captured by applying the PIV technique. The averaged vector elds as seen in gure 6 are superimposed with the image for a better visualization. This was processed using the DynamicStudio software. From gure 6 the averaged velocity proles in the vertical direction shows the Newtonian liquid ow in front of the bubble. The liquid is pushed upwards and the liquid which is owing around the bubble forms a falling lm. The averaged velocity elds presented here were determined from 20 instantaneous velocity elds. The same region was also processed using MatPIV. The time between two con-

Figure 6: Superposition of the average ow eld and a bubble image around the nose region of the Taylor bubble in water ows. secutive images captured by the high speed camera was 0.04s.

Figure 7 shows a superposition of a bubble image and an instantaneous velocity pro le around the nose region using 400 ppm PAC.

The velocity vectors are showing the intensity and the direction of the ow. This situation leads to the falling liquid thin lm between the pipe wall and the bubble.

5 Figure 6: Superposition of the average ow eld and a bubble image around the nose region of the Taylor bubble in water ows. secutive images captured by the high speed camera was 0.04s. The images was inverted in order for MatPIV to work. 100 µm of glass beads were used as seeding particles. Figure 7 shows a superposition of a bubble image and an instantaneous velocity pro le around the nose region using 400 ppm PAC. It can be seen from gure 7 that as the Taylor bubble moves upwards, the 400 ppm PAC solution in front of the bubble is pushed forward and away from the center. The velocity vectors are showing the intensity and the direction of the ow. This situation leads to the falling liquid thin lm between the pipe wall and the bubble. The bubble shape in Newtonian is di erent from that of non-newtonian uids at the bottom region of the bubble. High speed images used for PIV showing this di erence is represented in gure 8. For the PAC ows as seen in gure 8 (left) the bottom surface is more or less stable as the bubble rises. As the viscosity was increased, the trailing edge becomes more at. This was also observed by other authors1,2 in Carboxymethylcellulose (CMC) and Polyacrylamide (PAA) ows. A sequence of images from di erent Figure 7: Instantaneous velocity pro le superimposed with the bubble image around the nose region in PAC 400 ows. The image is inverted for clarity. Figure 8: Bottom region high speed images for 400 ppm PAC (left) and water ows. frames is presented in gure 9. It is from the recorded frame 3077 (left) to frame 3097 (right) in gure 9, possible to observe capillary wave. These waves appeared some time after the coalescence of the bubble with the surrounding liquid. From the high speed images the time between the frames 3077 to 3097 was 80ms corresponding to a 3.6cm lm length. This will give a wave velocity of 45cm/s. A visualization box is needed to measure the thickness as a function of uid viscosity as well as its dynamics. Small bubbles are present in the wake and tail several meters behind the Taylor bubble. This is re ected both in the

Figure 9: Sequence of frames showing capillary waves (encircled) in 400 ppm PAC ow. The time between frames is 40ms. high-speed images and in the P measurements.

Even for a very long pipe this pattern will be an integral part of the Taylor bubble regime, when its rise velocity exceeds a critical value determined by viscosity and surface tension.

6 Figure 9: Sequence of frames showing capillary waves (encircled) in 400 ppm PAC ow. The time between frames is 40ms. high-speed images and in the P measurements. These small bubbles are formed due to the jet and the wake instability at the trailing edge of the Taylor bubble. Even for a very long pipe this pattern will be an integral part of the Taylor bubble regime, when its rise velocity exceeds a critical value determined by viscosity and surface tension. Similar gures as illustrated in gure 3 and plotted in gure 5 (top) were expected both of 200 and 400 ppm PAC ows. However, during the experimental runs, electrical noise and / or grounding problems in the experimental hall impacted strongly on the pressure readings making the logged values improbable. As an example, 200 ppm PAC dissolved in water is presented in gure 10 using the same averaging method as mentioned earlier. It can be seen from gure 10 (top) that P 1 is essentially zero until at approximately 13s where the bubble was released. A sudden increase is observed followed by a decrease to reach a minimum. At the same time P 2 starts to decrease indicating that the bubble has passed the P 2 location. The P 2 which was expected to follow the same trend as in gure 5 (top) might have been exposed to erroneous signals, as mentioned, and therefore has too small negative amplitude. The Figure 10: P as a function of time (top) and the pressure applied to the bubble during release (bottom) for 200 ppm PAC ow. time of release is also shown in gure 10 (bottom) where the pressure decreases to approximately 300mbar. Pressures were recorded for approximately 80s. Although the same trend as seen in gure 3 and gure 5 is seen from gure 10, it is clear that the small bubbles in the wake of the Taylor bubble remains for a quite a long long time in PAC uids. This is reected as a longer relaxation time before the dierential pressures converge back to zero. PIV analysis of the falling lm is very dicult with the present setup, due to lack of an optical correction box. The intense light reection of the laser sheet in the bubble as well as in the pipe was very disturbing for the analysis. Although processing the images using grey scale and histogram processing, the appearance of these disturbances were still present. However, analyzing the high speed images frame by frame, it is possible to identify the position and velocity of a seeding particle that follow the bubble lm as a function of time. The result from such analysis is presented

in gure 11. This plot was produced by Figure 11: The position and speed (circled) of seeding particles following the falling lm in 400 ppm PAC ow. tracking the particles from approximately 70 frames.

The seeding particles are small and nearly immobile in the PAC uid above the Taylor bubble until they are reached by the bubble nose.

7 in gure 11. This plot was produced by Figure 11: The position and speed (circled) of seeding particles following the falling lm in 400 ppm PAC ow. tracking the particles from approximately 70 frames. The slug bubble velocity using high speed images was measured to be 31.5 cm/s which essentially matches the calculated velocity from the P data. The seeding particles are small and nearly immobile in the PAC uid above the Taylor bubble until they are reached by the bubble nose. It can be seen from gure 11 that the lm velocity accelerates from its minimum, i.e. just above the bubble, until close to position 9.5 cm, i.e. when the bubble has passed the eld of view. The velocities are calculated as the time derivative of the particle positions. The development of the falling lm from nose to tail is consistent with Sousa 1,2,5 et al. and with Bugg and Saad 10. It is in principle possible to calculate the thickness of the lm surrounding the Taylor bubble at any position based on the local lm velocity. The procedure is based on tracking selected seeding particles that follow the averaged lm velocity - a method still under development. A preliminary analysis of some particles in 400 ppm PAC ows indicates a ratio of terminal lm thickness to pipe radius equal to Published data from Bugg and Saad 10 for water indicate a value of CONCLUSIONS A ow rig for studying Taylor bubble dynamics propagating through a vertical tube has been constructed and used for the tests. The focus has been to study various section of the bubble pattern, in particular the nose and tail regions. The velocity of the bubble was measured both using PIV and by sets of differential pressures. The prediction of the rise velocity of the bubble was in good agreement with the results from P measurements. Tests indicate that the main eect of a sudden pressure release is that the Taylor bubble experiences a fast initial expansion leading to a liquid level rise in the pipe. This stage is then followed by a stabilized ow as in traditional stagnant liquid situations. The time required for stabilization depend on the liquid column height, and is associated with the time it takes to accelerate the liquid. 200 and 400 ppm of PAC dissolved in water have been used for demonstrating the eect of non-newtonian uid. The non-newtonian uids used for the tests are shear thinning. Generally, high viscosity uids give more stable bottom region of the Taylor bubble, i.e at edge, than water. This also causes less bubble production in the wake behind the Taylor bubble. On the other hand, the shear thinning property forces the smaller bubbles to remain in the wake for much longer time than for water. An interesting question from these two opposing trends then arises as to what rheology causes the least - or alternatively most bubbles - in the bubble wake. This may have important impact on uid fraction and pressure proles with relevance also to industrial applications. In this connection also quickly expanding bubbles behave dierently, since the wake is initially much more irregular. ACKNOWLEDGEMENTS The work was carried out at the Two

8 Phase Flow Laboratory at the University of Stavanger, Norway. Thanks are given to Svein Myhren for his valuable help in the signal instrumentations. The instrumentation for this work, laser and high-speed camera was granted from the Norwegian Research Council. REFERENCES 1. Sousa, R.G., Riethmuller, M.L., Pinto, A.M.F.R., Campos, J.B.L.M (2006), "Flow Around Individual Taylor Bubbles Rising in Stagnant Polyacrylamide (PAA) Solutions." J. Non- Newtonian Fluid Mech. 135, Sousa, R.G., Riethmuller, M.L., Pinto, A.M.F.R., Campos, J.B.L.M (2005), "Flow Around Individual Taylor Bubbles Rising in Stagnant CMC Solutions: PIV Measurements." Chemical Engineering Science, 60, pp Das, G., Das, P.K., Purohit, N.K., Mitra, A.K. (1998), "Rise Velocity of a Taylor Bubble Through Concentric Annulus." Chemical Engineering Science, 53,No. 5, pp Viana, F., Pardo, R., Yánez, R., Trallero, J.L., Joseph, D.D., (2003), "Universal Correlation for the Rise Velocity of Long Gas Bubbles in Round Pipes." J. Fluid Mech, Vol. 494, pp Sousa, R.G., Pinto, A.M.F.R., Campos, J.B.L.M (2007), "Interaction between Taylor bubbles Rising in Stagnant non-newtonian Fluids." International Journal of Multiphase Flow, 33, pp Rabenjamanantsoa, A.H., Time, R. and Saasen A. (2007), "Characteristic of the velocity proles over xed dunes in pipe", Annual Transactions of the Nordic Rheology Society, Vol. 14, DynamicStudio software version , DantecDynamics A/S 8. Sveen, J.K. (2004), "An Introduction to Mat- PIV." Version Eprint No. 2, ISSN , Department of Mathematics, University of Oslo. jks/matpiv. 9. Rabenjamanantsoa, A.H. (2007), "Particle Transport and Dynamics in Turbulent Newtonian and non-newtonian Fluids." PhD Thesis No. 36, ISBN University of Stavanger, Norway. 10. Bugg, J.D. and Saad, G.A (2002), "The Velocity Field Around a Taylor Bubble Rising in a Stagnant Viscous Fluid: Numerical and Experimental Results." International Journal of Multiphase Flow, 28, pp

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